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NASHVILLE - U.S. Sen. Lamar Alexander, R-Tenn., said Monday that President Barack Obama's call for U.S. military strikes punishing Syria's regime over alleged use of chemical weapons poses too many unknown risks and could backfire.

As a result, Alexander said he won't be voting for a resolution authorizing the U.S. to launch military strikes against Syria.

"I will vote 'no' because of too much uncertainty about what comes next," Alexander told the Nashville Rotary Club. "After Step A, what will be Steps B, C, D and E?"

He said he sees "too much risk that the strike will do more harm than good, by setting off a chain of consequences that could involve American fighting men and women in another long-term Middle East conflict."

In doing so, Alexander became one of several additional Republican and Democratic senators saying they won't support Obama's proposal.

Meanwhile, news reports out of Washington say Secretary of State John Kerry's suggestion that Syria could cede its chemical arms to avoid a strike quickly gaining traction with Russian President Vladamir Putin calling for Syrian chemical weapon depots to be placed under international control.

Obama later told CNN "we're going to take this seriously. But I have to emphasize that we have not seen ... these kind of positive gestures so far."

Earlier in the day, U.S. Rep. Chuck Fleischmann, R-Tenn., had returned to Washington where he was headed into a classified briefing by officials.

"I am certainly leaning 'no' for a lot of reasons," the congressman said, later adding, "I don't see any clear goals in regard to Syria, and I see the ... great potential of an escalation either in the region or globally."

His 3rd Congressional District constituents have overwhelmingly told him they don't want the resolution on any strike authorized.

Prior to Alexander's previously scheduled speech to Rotarians, state Rep. Joe Carr, Alexander's 2014 GOP primary opponent, took Alexander to task on being quiet on the issue. Carr opposes any strike.

"All we hear from Senator Alexander on this issue is crickets. I think the state of Tennessee is demanding, and will get, someone who is going to show leadership," Rep. Carr said in a statement.

Asked about the criticism, Alexander told reporters Carr can "say whatever he likes."

The senator said he spoke with top White House officials, including Kerry and the chairman of the Joint Chiefs of Staff, shortly after Obama's initial remarks on Aug. 31. Over the weekend, Alexander said, he spoke by phone with Defense Secretary Chuck Hagel.

Asked by reporters whether he had concerns U.S. credibility may be on the line, Alexander said he doesn't see that helped by what he called a "random military strike."

"America's credibility is better served by following the Colin Powell Doctrine, which is have a specific and clear objective related to a vital military interest, No. 1. No. 2, assemble an overwhelming force. And No. 3, have the stomach to see it all the way through to the end," Alexander said.

"I don't think any of those characteristics fits this proposed military strike," he added.

U.S. Rep. Scott DesJarlais, R-Tenn., has previously said he would oppose the use-of-force resolution.